Answer:
1. Rotation 90° counterclockwise
(x, y) → (-y, x)
2. Translation 2 right and 2 down
(x, y) → (x + 2, y – 2)
3. Reflection over the x-axis
(x, y) → (x, -y)
4. Translation 2 left and 2 up
(x, y) → (x – 2, y + 2)
Step-by-step explanation:
Translation 2 left and 2 up
To translate (move) a point two units to the left, we subtract 2 from its x-value. Similarly, to translate (move) a point two units up, we add 2 to its y-value.
(x, y) → (x – 2, y + 2)Rotation 90° counterclockwise
When rotating a point 90° counterclockwise, the y-value becomes negative, and the x and y switch:
(x, y) → (-y, x)Translation 2 right and 2 down
To translate (move) a point two units to the right, we add 2 to its x-value. Similarly, to translate (move) a point two units down, we subtract 2 from its y-value.
(x, y) → (x + 2, y – 2)Reflection over the x-axis
When a point is reflected over the x-axis, the y-value is negated but the x-value stays the same:
(x, y) → (x, -y)A rectangular plot of land is divided into 4 parcels
with integer dimensions (see the diagram, which is not to
scale). Parcels A and D are square plots with a combined
area of 898 ft.². Parcel B has an area of 351 ft.². How
wide is the rectangular plot of land?
A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a 0. If x + 20 = 0, then x must be -20.
What is quadratic equation?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a 0. Length + breadth equals the area of a rectangle. The length is 8 feet greater than the breadth in this instance since we are aware that it is 8 feet longer than its width. We may therefore write the length as x+8 if the width is x.
We may now express length and width as x•(x+8). We get x2 + 8x after multiplying.
We know that the area is 240 square feet but also that it is equal to x2 + 8x. So, x2 + 8x = 240. To get the equation, take 240 away from both sides.
x2 + 8x - 240 = 0.
The equation must now be solved. This can be accomplished by factoring, by applying the quadratic formula, or by solving the square. By factoring, I will demonstrate:
The formula for factoring x2 + 8x - 240 is (x + __)(x + ). The integers must be multiplied by -240 and added to equal 8.
Following are some number pairs that add up to -240:
-4 and 60-24 and 10-12 and 20Because they both sum up to 8, the numbers -12 and 20 are the ones we seek. -12•20 = -240, and -12 + 20 = 8.
We can factor x2 + 8x - 240 as (x - 12)(x + 20) as a result. Set each component to 0 in order to solve.
If x - 12 = 0, then x must equal 12.
If x + 20 = 0, then x must be -20.
The answers to the problem are 12 and -20, but neither of them makes sense. The solution -20 does not work since a rectangle's width cannot be negative. The width being 12 is the only answer that makes sense in this situation.
Consider what kind of form "width" is when choosing the units for width. 'Width' is a line. You use basic units, not squared or cubed units, for lines. The width measurement is therefore in feet.
The complete question is.
A regular plot of land has an area of 240 square feet and is 8 feet longer than its width....
a) Write a quadratic equation in the form ax2 + bx + c = , whose solution gives the width of the rectangular plot of land.
The equation for the width is blank (Type an equation. Type your answer in standard form)
b) Solve the equation.
The solution(s) to the quadratic equation found in part a is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed)
The width of the plot is blank (ft3, ft2, or ft?
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a pharmaceutical company wants to conduct a survey of individuals who have high cholesterol. the company has obtained a list from primary care physicians throughout the country of individuals who are known to have high cholesterol. design a sampling method to obtain the individuals in the sample. be sure to support the choice.
A good sampling method for this scenario would be a probability-based method called Simple Random Sampling.
In Simple Random Sampling, each individual from the population of individuals who have high cholesterol has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and that each individual in the population has a known non-zero probability of being selected.
This method can be supported by the fact that it is easy to implement, and it does not require any prior knowledge of the population characteristics. It also ensures that the sample is unbiased and has a good chance of being representative of the population.
Additionally, Simple Random Sampling is also a cost-effective sampling method as it is less expensive and time-consuming than other sampling methods such as stratified random sampling or cluster sampling.
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Approximately 10% of all people are left-handed ("11 little-known facts," 2013). consider a grouping of fifteen people. a.) state the random variable. x = ____________________________ b.) show that this is a binomial. find the probability that c.) none are left-handed. d.) seven are left-handed. e.) at least two are left-handed. f.) at most three are left-handed. g.) at least seven are left-handed. h.) find the mean of x. i.) find the variance of x. j.) find the standard deviation of x.
a) The random variable in this problem is the number of left-handed people in a grouping of 15 people.
x = number of left-handed people in a group of 15 people
Show that this is a binomial?b) This is a binomial experiment because it meets the following criteria:
The experiment consists of a fixed number of trials (15 people in this case)
Each trial has two possible outcomes (left-handed or not left-handed)
The probability of success (left-handed) is constant for each trial (10% or 0.1)
c) To find the probability that none are left-handed, we use the binomial probability formula:
P(x = 0) = (15 choose 0)(0.1)^0(0.9)^15 = 0.3429
d) To find the probability that seven are left-handed, we use the binomial probability formula:
P(x = 7) = (15 choose 7)(0.1)^7(0.9)^8 = 0.1540
e) To find the probability that at least two are left-handed, we need to find the probability of getting 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4) + ... + P(x = 15)
f) To find the probability that at most three are left-handed, we need to find the probability of getting 0, 1, 2, and 3 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
g) To find the probability that at least seven are left-handed, we need to find the probability of getting 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≥ 7) = P(x = 7) + P(x = 8) + P(x = 9) + ... + P(x = 15)
h) The mean of x is given by:
E(x) = 15(0.1) = 1.5
i) The variance of x is given by:
Var(x) = 15(0.1)(0.9) = 1.35
j) The standard deviation of x is given by:
SD(x) = √1.35 = 1.16
So, the mean of x is 1.5 and the standard deviation is 1.16. The probability of getting at least 2 left-handed people is 0.717, the probability of getting at most 3 left-handed people is 0.547 and the probability of getting at least 7 left-handed people is 0.0256.
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A person invests 4000 dollars in a bank. The bank pays 5.25% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5100 dollars?
The person must leave the money for 4 years and 8 months in the bank until it reaches 5100 dollars.
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
A person invests 4000 dollars in a bank.
The bank pays 5.25% interest compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.25/100
r = 0.0525 per year,
Then, solve the equation for t,
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(5,100.00/4,000.00) / (12 × [ln(1 + 0.0525/12)])
t = ln(5,100.00/4,000.00) / (12 × [ln(1 + 0.004375)])
t = 4.638 years
t = 4 years and 8 months.
Therefore, the time is 4 years and 8 months.
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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adults
ticket and the price of a child's ticket.
The price of an adult ticket is $20
The price of a child's ticket is $19
How to calculate the price of an adult and child ticket ?Let x represent the price of a child ticket
Let y represent the price of an adult ticket
Three adults and four children must pay 136
3y + 4x= 136.........equation 1
Two adults and three children must pay $97
2y + 3x= 97.........equation 2
From equation13 1
3y+4x= 136
3y= 136-4x
y= 136-4x/3
Substitute 136-4x/3 for y in equation 2
2(136-4x) + 3x= 97
272-8x/3 + 3x/1= 97
272-8x+9x/3= 97
cross multiply
272-8x+9x=291
collect the like terms
-8x+9x= 291-272
x= 19
Substitute 19 for x in equation 1
3y+4x= 136
3y + 4(19)= 136
3y+ 76= 136
3y= 136-76
3y=60
y= 60/3
y= 20
Hence children tickets cost $19 and adult tickets cost $20
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her budget is still $50 a month. to find out how many gigabytes of data she could use if she chose this plan, she writes c(x)
The function that represents the total cost for the number of gigabytes is; C(x) = 50x
How to express linear equation word problems?Some of the steps to writing a system of linear equations from word problems are;
1) Understand the problem like the words used in stating the problem and what exactly you are trying to find.
2) Translate the problem to an equation by assigning a variable (or variables) to represent the unknown.
3) Carry out the plan and solve the problem.
We are told that her budget is $50 a month. Therefore this is like the rate for each gigabyte and if the number of gigabytes is denoted as x, then the function of the total cost is;
C(x) = 50x
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what is the difference between using the unit rate to find how many feet are in a given number of inches and using the unit rate to find how many inches are in a given number of feet
For feet we will divide the given no. of inches by 12 and for inches we will multiply the given number of feet by 12.
What is feet and inches?Since 1 foot is equal to 12 inches, the given value (in feet) is converted to inches by multiplying by 12. To compare lengths given in different units or to perform arithmetic operations on them, it is crucial to learn how to convert feet to inches (ft to in).
We know that 1 feet = 12 inches.
And to find how many feet are in a given number of inches
We will divide the given no. of inches by 12.
And
To find how many inches are given in a number of feet
We will multiply the given number of feet by 12.
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What is the slope of the line that contains the points (2, -8) and (-4, 4)?
2
1/2
-1/2
-2
Option D) The slope of the line that contains the points (2, -8) and (-4, 4) is -2
What is a slope ?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Slope is give by 2 points on a line is [tex]\frac{y\x_{2}- y\x_{1} }{x_{2}-x_{1}}[/tex]
so the slope is
[tex]\frac{4 - (-8)}{-4 - 2} = \frac{12}{-6} = -2[/tex]
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What topics are introduced in Algebra 2?
Answer:
Algebra 2 typically builds on the concepts covered in Algebra 1 and introduces more advanced topics such as:
Quadratic equations and functions
Complex numbers
Polynomial functions and their operations
Rational functions and their operations
Conic sections
Exponential and logarithmic functions
Sequences and series
Trigonometry
Matrices and determinants
Permutations and combinations
Probability
Functions and relations
Limits and derivatives
Answer:
rrtgf thing for them code mine took also
3
Step-by-step explanation:
tutfd
jessie worked 22 hours last week at the auto shop and earned 242 dollars. if she continues at the same hourly pay, how many more hours must she work to earn an additional 154 dollars
On solving the provided question, we can say that by unitary method 14 more hours must she work to earn an additional 154 dollars
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
jessie worked = 22 hours last week at the auto shop
shop and earned = 242 dollars
1 hour = 242/22
154 dollars = 22/242*154 = 0.0909090909 * 154 = 13.9999999986 = 14 hours
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Please help explain with how you got the answer step by step
Answer:
B
Step-by-step explanation:
You solve all until you get the exact expression being found.
(x-7)(x+2) Step.1 ) Distribute Multipliciation
=X^2 +2x -7x -14. Step 2.) Add like terms
=X^2 -5x -14. Step 3.) Solve
Final Answer: B
Now you're going to imagine that you invested $1,000 in a company one year ago, and you want to see how well your investment would be doing today.
To begin, choose a company that you're familiar with and that seems as if it might be a good investment - that is, a company that you think will have rising stock prices. Think about companies that you use or know are popular Remember, not all companies are public companies. You'll need to check the New York Stock Exchange to find out if you can actually buy shares in this company Once you've settled on a company, find its stock price from one year ago and for today Write a journal entry about your imagined investment Answer the following questions as you write
1.) What stock did you buy?
2.) Why did you think buying this stock would be a good idea?
3.) How much would you have made or lost on an investment of $1,000?
(Hint First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today Compare that to your initial investment of $1,000)
4.) Could you have made more money by selling sooner?
Answer:
Step-by-step explanation:
1. What stock did you buy?
Apple Inc.
2. Why did you think buying this stock would be a good idea?
Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.
3. How much would you have made or lost on an investment of $1,000?
I would have made $105.
Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.
4. Could you have made more money by selling sooner?
Yes, on October 3, 2018 it was at its peak for the year.
your investment would be doing great today. you would make $115 from the given investment.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Given, you're going to imagine that you invested $1,000 in a company one year ago
I will buy the stocks of amazon.The popularity of Amazon products is rising daily. The business frequently introduces cutting-edge technology. I was confident that it would be a secure investment.I would have made $115.Hint: To start, divide $1,000 by the stock's current price, one year ago, to see how many shares you might have purchased. It can be necessary to infer the stock price from the graph. The number of shares should be rounded up to the next whole number. Then, multiply the number of shares you purchased by the stock's current price to determine the share's current worth. Contrast that with your $1,000 original investment.on September 5, 2022, it was at its peak for the year.Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.
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In a sale, the price of a TV is reduced from £250 to £180 what is the decreased percentage?
Answer:
Step-by-step explanation: 80
Answer: THE ANSWER IS 28%
worked it out on the calculator in the end
Step-by-step explanation:
let f be the function with derivative given by f'(x)=x^2-2/x. On which of the following intervals is f decreasing ?
A. (- [infinity], -1] only
B. (- [infinity], 0)
C. [- 1,0) only D. (0, ∛2]
E. (∛2, [infinity])
Therefore, the function f is decreasing on the interval (- [infinity], -1].
A. (- [infinity], -1] only
We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.
For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.
We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.
Therefore, the function f is decreasing on the interval (- [infinity], -1].
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find the area of the shaded triangle
Answer:
20cmStep-by-step explanation:
4x10 40 divided by 2help with this question
Answer:
distance from beginning is 225 and the change is -65 per hour
Step-by-step explanation:
At a community barbecue, Mrs. Vance and Mr. Coleman are buying dinner for their families. Mrs. Vance purchases 1 hot dog meal and 3 hamburger meals, paying a total of $36. Mr. Coleman buys 2 hot dog meals and 2 hamburger meals, spending $32 in all. How much do the meals cost?
The cost of one hamburger meal is $10 and the cost of one hot dog meal is $6.
What is the cost of one meal?The first step is to form a system of equations using the information in the question:
a + 3b = 36 equation 1
2a + 2b = 32 equation 2
Where:
a = cost of one hot dog meal
b = cost of one hamburger meal
The elimination method would be used to determine the cost of each meal
Multiply equation1 by 2
2a + 6b = 72 equation 3
Subtract equation 2 from equation 3
4b = 40
Divide both sides of the equation by 4
b = 40 / 4
b = 10
Substitute for b in equation 1:
a + 3(10) = 36
a + 30 = 36
a = 36 - 30
a = 6
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Is dividing by 1 2 the same as dividing in half?
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately). No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively. For example, if we have the number 10, dividing by 1/2 would give us 5 (10/2), while dividing by 1 and 2 would give us 5 and 5 (10/1 = 10 and 10/2 = 5).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
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There are four typical measures of the central tendency of a frequency distribution. Which of the following is NOT ameasure of central tendency?a. meanb. medianC moded. method of least squares
method of least squares is not a measure of central tendency which is not involved in the typical measures.
The central tendency of the dataset are defined as three important measures namely mean, median and mode. The mean shows the average value of the dataset. which can be calculated as the sum of all the values in the dataset which are divided by the number of values. and it is considered as the arithmetic mean. Some of the other measures of mean which is used to find the central tendency are as mentioned as:
Geometric Mean , Harmonic Mean ,Weighted Mean.
Median is the middle value of the dataset in which the it is arranged in the ascending order or in descending order. When the dataset which contains an even number of values, then the median value of the dataset can be calculated by taking the mean of the middle two values.
The mode shows the frequently occurring value in the dataset. Sometimes the dataset are arranged and which contain multiple modes and in some situations , it does not contain any mode at all.
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[tex]\frac{x+5}{x+9}+\frac{x+7}{x^{2}-9}÷\frac{x^{2}-9}{x+3}[/tex]
The result for the division of the fractions in this problem is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
How to divide two fractions?The division of two fractions is given by the multiplication of the first fraction by the inverse of the second fraction.
The first fraction in this problem is composed by the sum of two fractions, as follows:
[tex]\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}[/tex]
Applying the subtraction of perfect squares, we have that:
x² - 9 = (x - 3)(x + 3).
The second fraction is given as follows:
(x² - 9)/(x + 3).
Considering the factoring of x² - 9, the second fraction is given as follows:
x - 3.
Hence the inverse is of:
1/(x - 3).
Then the entire quotient is given as follows:
[tex]\left(\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}\right) \times \frac{1}{x - 3}[/tex]
The addition of the two fractions is given as follows:
[tex]\frac{(x + 5)(x^2 - 9) + (x + 7)(x + 9)}{(x + 9)(x^2 - 9)} = \frac{x^3 + 6x^2 + 7x + 18}{(x + 9)(x^2 - 9)}[/tex]
Applying the multiplication by x - 3 in the denominator, the quotient is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
Missing InformationThe problem asks for the quotient between the two fractions.
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The temperature is 8 degrees Fahrenheit. It is expected to fall 5 degrees each hour for the next several hours. Write and solve and equation to find how many hours will it take for the temperature to reach negative 7 degrees fahrenheit?
Answer:
8-5x=-7 , answer is 3hours
Step-by-step explanation:
Start with the current temperature 8 degrees
Then use x to represent the hours of the temperature dropping x
Then set it equal to the temperature you want to reach -7
So 8-5x=-7
To solve get the x alone so subtract 8 form both sides
-5x=-15
And then solve
X=3
Find the equation of the line.
Use exact numbers.
y=y=y, equals
x+x+x, plus
\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9yyxx
On solving the provided question, we can say that Slope is 1/2, so equation is y=1/2x+0 or y=1/2x.v
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
We can utilize the slope-intercept version of the equation. It is written as y=mx+b. B is the y-intercept, and m stands for the slope. The line intersects the y-axis at (0,0). the y-intercept is consequently 0.
the slope by equation, we have
m = y2 - y1 / x2 - x1
m = 2-1/4-2
m = 1/2
Slope is 1/2, so equation is y=1/2x+0 or y=1/2x.
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The correct question is
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus 5
The distance, d, in miles that a person can see to the horizon can be modeled by the formula d = radical 3h/2 where h is the person's height above sea level in feet. How far to the horizon can a person see if they are 1,000 feet above sea level?
Answer: To find the distance a person can see to the horizon when they are 1,000 feet above sea level, we can substitute h = 1000 into the formula d = radical 3h/2
d = radical 3(1000)/2 = radical 3(1000*2) = radical 6000
d = radical 6000 = 77.46 miles
So if a person is 1,000 feet above sea level, they can see 77.46 miles to the
Step-by-step explanation:
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone. Which are equivalent equations?
The formula of lateral area of a cone can be equivalent to the formulas:
LA = r√(r^2 + h^2) and
LA = πrl
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.
The slant height (s) of a cone is the distance from the apex of the cone to the center of the base along a line that is perpendicular to the base and passes through the apex. The slant height of a cone can be found using the Pythagorean theorem using the radius (r) and the height (h) of the cone:
s = √(r^2 + h^2)
So, the formula for lateral area of a cone can be equivalent to the formula:
LA = r√(r^2 + h^2)
Another equation that is equivalent to the lateral area formula is
LA = (1/2)(2πr)(l)
LA = πrl
where l is the slant height of the cone.
This is because the lateral area of a cone is equal to (1/2) of the circumference of the base multiplied by the slant height, and we know that the circumference of a circle is equal to 2πr.
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comment calcule t'on (4x+5)²−25=0
Answer:
x = 0 and
x = -(5/2)
Step-by-step explanation:
(4x+5)²−25=0
(16x^2+40x + 25) - 25 = 0 [expand the square]
16x^2+40x = 0
8x(2x+5)=0
the roots are 8x=0 and 2x+5 = 0
x = 0 and x = -(5/2)
suppose we select every fifth invoice in a file. what type of sampling is this?
Select one:
a. Random
b. stratified
c. cluster
d. systematic
We select every fifth invoice in a file is systematic sampling.
'What is systemic sampling?'
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).
This method will provide you with a representative sample that can be utilized to make inferences about your community of interest if the population order is random or random-looking (for example, alphabetical).
Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out. Similar to basic random sampling, systematic sampling can be used using a list of every member of the population. Contrary to simple random sampling, however, you can also utilize this strategy if you don't have access to a list of your population in advance.
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if x+3/3=y+2/2 then x/3=
a. y+1
b. y/3
c. y/2
d. y-1
The fraction is :
[tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex] then :[tex]\frac{x}{3} = \frac{y}{2}[/tex]
The correct option is (c).
Now, According to the question:
The given fraction is :
[tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex]
To solve the above fraction and find x/3 =?
We can solve this by cross-multiplying.
Since [tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex] ,we can cross-multiply both sides of the equation to remove the denominators.
Multiple the right side by 2 and the left side by 3 to get 2(x+3)=3(y+2).
Distribute to get the x on one side. 2x+6=3y+6.
The 6s on both sides cancel out so we are left with
2x=3y.
Divide both sides by 2 to get x on one side, so x= 3y/2
The question asks for x/3,
so we can divide both sides of the equation to get:
[tex]\frac{x}{3} = \frac{3y}{6}[/tex]
Simplify, We get:
[tex]\frac{x}{3} = \frac{y}{2}[/tex]
Hence, (c) is the correct answer.
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A realtor wishes to enclose 600 of land in a rectangular plot and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the rectangular plot that require the least amount of fencing
The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Now, According to the question:
Optimization using Derivatives:
Suppose the function F(x) has continuous first- and second-order derivatives, F′(x) and F″(x).
At a point x=c in the domain of F(x), the function:
has a relative minimum if F′(c)=0 (critical point) and F″(c)>0 (concave up); and,has a relative maximum if F′(c)=0 (critical point) and F″(c)<0 (concave down).600 [tex]u^2[/tex] of land to be enclosed by fence
Area inside plot should be maximized, amount of fence should be minimized
If we draw a quick sketch, we get something like this:
_____ _____
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The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.
Let's put some variables into our picture so we can define our constraints.
y y
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x | x | x |
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Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.
A = x × 2y = area = 600
P = 3x + 4y = perimeter = a minimum
First we solve the area equation for y:
y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]
and then we substitute that result into our perimeter equation:
P = 3x + 4 (300/x)
P = 3x + 1200/x
Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]
We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.
In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is
P'(x) = 3 - 1200[tex]x^-^2[/tex]
When set equal to zero, we can solve for x:
3 - 1200[tex]x^-^2[/tex]= 0
1 - 400[tex]x^-^2[/tex] = 0
1 = 400/[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 400
x = ± 20
Our fence length can't be a negative number so our answer must be 20u.
If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.
The y length is 300/(20) = 15
Let's put all of our numbers into our picture to see if it make sense.
15 15
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20 | 20 | 20 |
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15 15
Sure enough our area is 600.
Here's what we have right now:
A(20, 15) = 600
P(20, 15) = 120
How about we try something a little bigger like 20.5 for x and 14.63 for y?
A(20.5, 14.63) = 600
P(20.5, 14.63) = 120.02
How about we try something a little smaller like 19.5 for x and 15.38 for y?
A(19.5, 15.38) = 600
P(19.5, 15.38) = 120.02
It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.
You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.
Each rectangle is 300[tex]u^2[/tex]. We want a square so each side would be √(300) = 17.32
17.32 17.32
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17.32 | 17.32 | 17.32 |
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17.32 17.32
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Hence, The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
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The velocity of a drone, during the first minute of flying, is recorded in the table below. Time (seconds) 0 10 20 30 40 50 60 Velocity (ft./sec) 20 22 26 30 36 34 32Using the left-hand rectangular approximation method (LRAM), what is the approximate total distance the drone flies during the first minutea. 1.480 ftb. 1.680 ftc. 1.800 ftd. 4.780 ft
Answer: 1680 ft
Step-by-step explanation:
See attachment
Why is absolute value always positive or zero?
The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.
The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.
Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }
if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.
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